Answer:
Explanation:
V=ds/dt
Where s =distance traveled
Given
V= 2ti - 3t²j
ds/dt=2ti - 3t²j
ds=(2ti - 3t²j)dt
Integrating
S= 2t²i/2 - 3t³j/3 + C
S=t²i - t³j + C
Since the object starts from Rest when t=0 and s(distance)=0
0=0²i - 0³j + C
C=0
Therefore
S=t²i - t³j
At t=2sec
S=(2)²i - (2)³j
S=4i - 8j
Magnitude of S(distance) = √4²+(-8)²
S= 4√5 meters
S=8.94meters.
2.mass =2kg
F(t)=5e^-0.1t
From Newton 2nd Law
F(t) = mdv/dt
5e^-0.1t= 2dv/dt
2dv = (5e^-0.1t)dt
Integrating
2V(t) = 5e^-0.1t/(-0.1) + C
2v(t) = - 50e^-0.1t + C
Since it started from rest at t=0. That is v(0)=0
2(0) = -50e^-0.1(0) + C
0 = -50 + C
C= 50
v(t) = -50e^-0.1t + 50
At t=10sec
v(10) = -50e^-0.1(10) + 50
V= -18.39 + 50
V= 31.61ms-¹.
While using your calc to evaluate -50e^-0.1(10)
Don't forget the -(minus) sign at the top of the exponential.
If you neglect it... You'll have a different answer.
Hope this helps.
Have a great day!!!
a car runs of a road and collides with a tree. glass pieces from the windscreen are projected forward and are found an average distance of 12m from the car. the average height of the windscreen is 1.2m.
Establish the speed of the car at the time of impact. assume g=10 m/s²
Answer:
v₀ₓ = 24.24 m / s
Explanation:
This is a projectile launching exercise, where the windshield comes out with a horizontal initial velocity.
Y axis
initial vertical velocity is zero
y = y₀ + v_{oy} t - ½ g t²
when it reaches the ground its height is zero and the initial height is y₀=1.2m
0 = y₀ + 0 - ½ g t²
t = [tex]\sqrt{2 y_o/g}[/tex]
t = [tex]\sqrt{2 \ 1.2 / 9.8}[/tex]
t = 0.495 s
X axis
x = v₀ₓ t
v₀ₓ = x / t
v₀ₓ = 12 / 0.495
v₀ₓ = 24.24 m / s
A circular wire loop is placed near a long, straight, current-carrying wire in which the current is either increasing or decreasing. Draw the situations in which the induced current in the loop counterclockwise?
Answer:
The induced current is counter clockwise if the current is decreasing and towards right.
Explanation:
When the current is decreasing in the wire, the direction of magnetic field at the center of the loop is outwards to the plane of paper which is given by the Maxwell's right hand thumb rule. The magnetic field is decreasing in nature.
So according to the Lenz's law, the induced current is such that which opposes the cause of its production, so that the induced current is counter clockwise.
40 ohms
1.2 A
40 ohms
12 V
Calculate the total energy developed in 5
minutes by the system above.
Answer:
17280 J and 1080 J
Explanation:
Given :
R= 40 ohm
I=1.2A
t= 5 min=60×5=300 sec
Now,
Total energy can be calculated as:
[tex]E=I^{2} Rt\\E=(1.2)^{2} *40*300\\E=17280 J[/tex]
Now,
V=12V
R=40 Ohm
[tex]E=\frac{V^{2} }{R} *t\\E=\frac{(12)^{2} }{40} *300\\E=1080 J[/tex]
Total energy is 17280 J and 1080 J
How is fitness walking beneficial?
It can relieve stress and improve mood.
It can decrease energy levels.
It can decrease perspiration.
It can relieve allergy symptoms.
Answer:
It can relieve stress and improve mood.
help plzzzzzzzzzzzz ?
Explanation:
1. First, let's find the total resistance of the circuit. We begin by combining [tex]R_{4}[/tex], [tex]R_{5}[/tex] and [tex]R_{6}[/tex]:
[tex]R_{456}=R_{4} + \dfrac{R_{5}R_{6}}{R_{5} + R_{6}}[/tex]
[tex]= 6\:Ω + \dfrac{(3\:Ω)(5\:Ω)}{3\:Ω+5\:Ω} = 7.9\:Ω[/tex]
Now time to combine [tex]R_{2}[/tex] and [tex]R_{3}[/tex] and they are connected in series so
[tex]R_{23} =R_{2} + R_{3} = 17\:Ω[/tex]
Note that [tex]R_{23}[/tex] and [tex]R_{456}[/tex] are connected in parallel so
[tex]R_{23456} = \dfrac{R_{23}R_{456}}{R_{23}+R_{456}}=5.4\:Ω[/tex]
Finally, [tex]R_{23456}[/tex] is connected in series with [tex]R_{1}[/tex] so the total resistance [tex]R_{T}[/tex] is
[tex]R_{T} = R_{1} + R_{23456} = 10\:Ω + 5.4\:Ω = 15.4\:Ω[/tex]
2. The total current in the circuit is
[tex]I_{T} = \dfrac{V}{R_{T}} = \dfrac{20\:V}{15.4\:Ω} = 1.3\:A[/tex]
3. The voltage drop across [tex]R_{1},\:V_{1}[/tex] is
[tex]V_{1} = I_{T}R_{1} = (1.3\:A)(10\:Ω) = 13\:V[/tex]
4. We can see that [tex]I_{T} = I_{1} + I_{2}[/tex]. To solve for [tex]I_{1}[/tex], we need [tex]V_{23}[/tex], which is just [tex]V_{T} - V_{1} = 20\:V - 13\:V = 7\:V[/tex] , which gives us
[tex]I_{1} = \dfrac{V_{23}}{R_{23}} = \dfrac{7\:V}{17\:Ω} = 0.4\:A[/tex]
5. From #2 & #4, [tex]I_{2} = 1.3\:A - 0.4\:A = 0.9\:A[/tex] and we also know that the voltage drop across [tex]R_{456}[/tex] is 7 V, the same as that of [tex]R_{23}[/tex]. The voltage drop across [tex]R_{4}[/tex] is
[tex]V_{4} = I_{2}R_{4} =(0.9\:A)(6\:Ω) = 5.4\:V[/tex]
This means that the voltage drop across [tex]R_{6}[/tex] is 7 V - 5.4 V = 1.6 V. Knowing this, the current through [tex]R_{6}[/tex] is
[tex]I_{6} = \dfrac{1.6\:V}{5\:Ω} = 0.3\:A[/tex]
Rest and Motion are the relative term. why? explain with example(please help me (╥﹏╥))
Explanation:
it depens on the subject and object. Let's example
you are driving a tesla car with your dog sitting on your side. You will say that the dog is at REST
but your friend, standing in sidewalk, seeing the same dog, will say that your dog is moving because it has MOTION from your car
Instantaneous speed is...
a) A speed of 1000 km/h
b) The speed attained at a particular instant in time.
c) The speed that can be reached in a particular amount of time.
PLEASE HURRY
Answer:
The speed attained at a particular instant in time.
Explanation:
Instantaneous speed is the speed attained at a particular instant in time.
It is given by :
[tex]v=\dfrac{dx}{dt}[/tex]
It is equal to the rate of change of speed.
It can be also defined as when the speed of an object is constantly changing, the instantaneous speed is the speed of an object at a particular moment (instant) in time.
Hence, the correct option is (b).
What is the magnitude of the resultant velocity for a bird flying first at a
speed of 10 m/s North East and then flying to South at a speed of 8 m/s?
Answer:
the magnitude of resultant is landify space ociured by meteroid
The magnitude of resultant velocity for a bird flying is 7.132 m/s.
What is Velocity?Velocity is defined as the directional motion of an object which is observed from a particular frame of reference and measured by a particular standard of time, as an indication of the rate of change of position.
Velocity is the Vector quantity as it has magnitude as well as direction. It can be represented as
[tex]\overline{v}={\frac{\Delta x}{\Delta t}}[/tex]
[tex]\overline{v} = average velocity[/tex]
[tex]{\Delta x} = displacement[/tex]
[tex]{\Delta t} = change in time[/tex]
For the information above, two vectors are represented as the sides of a parallelogram, then the resulting vector is given as the diagonal of that parallelogram. The resultant vector is that it can have any value between a maximum and a minimum depending on the angle; But scalar numbers can have either maximum or minimum value depending on whether they are added or subtracted.
The resultant vector of any two vectors is given by: [tex]v^2= \sqrt{v_1^2+ v_2^2+ 2 v_1v_2 cos }[/tex]Θ
where, Θ is the angle between these two vectors.
The angle between directions north-east and south is 135°.
So, the magnitude of the resultant vector is
[tex]v= \sqrt{10^2 + 8^2 +2.10.8. cos 135}[/tex]
v= 7.132 m/s
Thus, the magnitude of resultant velocity for a bird flying is 7.132 m/s.
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They create a heat engine where the hot reservoir is filled with water and steam at equilibrium, and the cold reservoir is filled with ice and water at equilibrium. What is the Carnot efficiency for their heat engine if the pressure is constant at 1.0 atmospheres?
Answer:
The efficiency of Carnot's heat engine is 26.8 %.
Explanation:
Temperature of hot reservoir, TH = 100 degree C = 373 K
temperature of cold reservoir, Tc = 0 degree C = 273 K
The efficiency of Carnot's heat engine is
[tex]\eta = 1-\frac{Tc}{T_H}\\\\\eta = 1 -\frac{273}{373}\\\\\eta = 0.268 =26.8 %[/tex]
The efficiency of Carnot's heat engine is 26.8 %.
A 17-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 33 N. Starting from rest, the sled attains a speed of 1.6 m/s in 9.8 m. Find the coefficient of kinetic friction between the runners of the sled and the snow.
Answer:
[tex]\mu=0.185[/tex]
Explanation:
From the question we are told that:
Mass [tex]m=17kg[/tex]
Force [tex]F=33N[/tex]
Velocity [tex]v=1.6m/s[/tex]
Distance [tex]d= 9.8m[/tex]
Generally the equation for Work done is mathematically given by
[tex]W=\triangle K.E+\triangle P.E[/tex]
Where
[tex]\triangle K.E=(F-F_f)*2[/tex]
[tex]F_f=F+\frac{\triangle K.E}{d}[/tex]
[tex]F_f=33+\frac{0.5*17*1.6^2}{9.8}[/tex]
[tex]F_f=30.8N[/tex]
Since
[tex]f = \mu*m*g[/tex]
[tex]\mu= 30.8/(m*g)[/tex]
[tex]\mu= 30.8/(17*9.81)[/tex]
[tex]\mu=0.185[/tex]
Why do some "people" still believe that the earth is "flat".
I called my brother in Australia and it was day here, and night there, HOW CAN THE EARTH POSSIBLY BE FLAT, i did a zo,om meeting to prove that it was live. WHAT ARE PE,OPLE TH,INKING!!!
Answer: Members of the Flat Earth Society claim to believe the Earth is flat. Walking around on the planet's surface, it looks and feels flat, so they deem all evidence to the contrary, such as satellite photos of Earth as a sphere, to be fabrications of a "round Earth conspiracy" orchestrated by NASA and other government agencies.
♛ Mark me as Brainliest if I’m right
which describes a homogeneous mixture
Answer:
A homogeneous mixture is a type of mixture in which the composition is uniform and every part of the solution has the same properties. Example, air
Explanation:
An Na ion has a charge of +1 and an Oion has a charge of -2. How many Na ions does one Oion need to balance
charges?
Explain the meaning of work done and give examples
Answer:
the situation in which the force or any kinds of things rhat are done by force is called work done.ex.typed,wrote
Answer:
WORK DONE on a body is the product ofFORCE IN THE DIRECTION OF DISPLACEMENT AMD DISPLACEMENT.WORK ONLY HAS MAGNITUDE AND NO DIRECTION.
FORCE applied IN the direction of displacement × displacement = POSITIVE WORK DONEFORCE applied OPPOSITE to the direction of displacement × displacement = NEGATIVE WORK DONEFORCE applied PERPENDICULAR to the direction of displacement × displacement = ZERO WORK DONEhope it helps
have a nice day
Hooke's law describes a certain light spring of unstretched length 38.0 cm. When one end is attached to the top of a door frame and a 6.00-kg object is hung from the other end, the length of the spring is 42.0 cm.
a. Find its spring constant.
b. The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 150 N. Find the length of the spring in this situation.
Answer:
(a) 1470 N/m
(b) 48.2 m
Explanation:
Applying,
(a) F = ke.................... Equation 1
Where F = force applied to the spring, k = spring constant, e = extension
make k the subject of the equation
k = F/e............... Equation 2
But,
F = mg............. Equation 3
Where m = mass, g = acceleration due to gravity
Substitute equation 3 into equation 2
k = mg/e.............. Equation 4
From the question,
Given: m = 6 kg, e = 42-38 = 4 cm = 0.04 m
Constant: g = 9.8 m/s²
Substitute these values into equation 4
k = (6×9.8)/0.04
k = 1470 N/m
(b) Consider the end of the spring to the left which exert a force to the right
Then,
e = F/k............. Equation 5
Given: F = 150 N, k = 1470 N/m
Substitute these values into equation 5
e = 150/1470
e = 0.102 m
Hence the length of the spring is
L = 0.38+0.102 = 0.482 cm = 48.2 m
The geometric shape of the molecule H2,O. A. bent B. Trigonal planar C. linear D. t shape
Answer:
A. bent
Explanation:
Water molecule (H2O) is said to contain four valence electron pairs (2 bond pairs and 2 lone pairs). The presence of lone pair of electrons in the water molecule influences its molecular geometry or shape.
Since water has two lone pairs of electrons, which repel each other according to the VSEPR theory, water molecule is said to have a BENT molecular geometry.
Hank and Harry are two ice skaters whiling away time by playing 'tug of war' between practice sessions. They hold on to opposite ends of the same rope and pull the other toward him. The magnitude of Hank's acceleration is 1.26 times greater than the magnitude of Harry's acceleration. What is the ratio of Hank's mass to Harry's mass?
Answer:
the ratio of Hank's mass to Harry's mass is 0.7937 or [ 0.7937 : 1
Explanation:
Given the data in the question;
Hank and Harry are two ice skaters, since both are on top of ice, we assume that friction is negligible.
We know that from Newton's Second Law;
Force = mass × Acceleration
F = ma
Since they hold on to opposite ends of the same rope. They have the same magnitude of force |F|, which is the same as the tension in the rope.
Now,
Mass[tex]_{Hank[/tex] × Acceleration[tex]_{Hank[/tex] = Mass[tex]_{Henry[/tex] × Acceleration[tex]_{Henry[/tex]
so
Mass[tex]_{Hank[/tex] / Mass[tex]_{Henry[/tex] = Acceleration[tex]_{Henry[/tex] / Acceleration[tex]_{Hank[/tex]
given that; magnitude of Hank's acceleration is 1.26 times greater than the magnitude of Harry's acceleration,
Mass[tex]_{Hank[/tex] / Mass[tex]_{Henry[/tex] = 1 / 1.26
Mass[tex]_{Hank[/tex] / Mass[tex]_{Henry[/tex] = 0.7937 or [ 0.7937 : 1 ]
Therefore, the ratio of Hank's mass to Harry's mass is 0.7937 or [ 0.7937 : 1 ]
What actually heats up the atmosphere?
Answer:
The heat source for our planet is the sun. Energy from the sun is transferred through space and through the earth's atmosphere to the earth's surface. Since this energy warms the earth's surface and atmosphere, some of it is or becomes heat energy.
How does the magnitude of the normal force exerted by the ramp in the figure compare to the weight of the static block? The normal force is:______ a. greater than the weight of the block. b. possibly greater than or less than the weight of the block, depending on whether or not the ramp surface is smooth. c. equal to the weight of the block. d. possibly greater than or equal to the weight of the block, depending on whether or not the ramp surface is smooth. less than the weight of the block.
Answer:
less than the weight of the block.
Explanation:
From the free body diagram, we get.
The normal force is N = Mg cosθ
The tension in the string is T = Mg sinθ
Wight of the block when the block is static, W = Mg
Now since the magnitude of cosθ is in the range of : 0 < cosθ < 1,
therefore, the normal force is less than the weight of the static block.
3) show thal escape veloerty ve where symbols have their usual meaning?
Answer:
[tex]v = \sqrt{\frac{2GM}{r} }[/tex]
The formula for escape velocity where:
G - Gravitational constant (9.81 etc.)
M - the mass of the object the escape should be made from
r - distance to the centre of that mass
Which of the following is a good example of a contact force?
ОА.
Earth revolving around the Sun
OB.
a bridge suspended by cables
OC.
a ball falling downward a few seconds after being thrown upward
OD. electrically charged hairs on your head repelling each other and standing up
Answer:
A bridge suspended by cables
Explanation:
Both objects represent a contact force (in this case, normal force) acting on each other. The force occurs since both objects are in direct physical contact.
Một vật chuyển động tròn đều có chu kì T = 0,25 s. Tính tần số chuyển động f của vật?
Explanatio
omega=2pi/T
Answer:
0
0000
Explanation:
A clay vase on a potter's wheel experiences an angular acceleration of 7.24 rad/s2 due to the application of a 13.3-N m net torque. Find the total moment of inertia of the vase and potter's wheel.
Answer:
[tex]I=1.83\ kg-m^2[/tex]
Explanation:
Given that,
The angular acceleration of the wheel,[tex]\alpha =7.24\ rad/s^2[/tex]
Net torque,[tex]\tau=13.3\ N-m[/tex]
We need to find the total moment of inertia of the vase and potter's wheel. We know that,
Net torque,[tex]\tau=I\alpha[/tex]
Where
I is the moment of inertia
So,
[tex]I=\dfrac{\tau}{\alpha }\\\\I=\dfrac{13.3}{7.24}\\\\I=1.83\ kg-m^2[/tex]
So, the moment of inertia of the vase is equal to [tex]1.83\ kg-m^2[/tex].
A 1,500-kg truck has a net force of 4,200 N acting on it . What is the trucks' acceleration
Answer:
2.8 m/s²Explanation:
The acceleration of an object given it's mass and the force acting on it can be found by using the formula
[tex]a = \frac{f}{m} \\ [/tex]
f is the force
m is the mass
From the question we have
[tex]a = \frac{4200}{1500} = \frac{42}{15} \\ = 2.8[/tex]
We have the final answer as
2.8 m/s²Hope this helps you
An airplane is traveling at 940 km/h. How long does it take to travel 2.00 km?
Answer:
Explanation:
Since the path an airplane travels is pretty much horizontal, then acceleration in this dimension is 0 and the equation we use is strictly the d = rt one. Here we use it and solve for t:
[tex]t=\frac{d}{r}[/tex] and filling in:
[tex]t=\frac{2.00}{940}[/tex] so
t = .002 hrs which is the same as 7.2 seconds
Matthew throws a ball straight up into the air. It rises for a period of time and then begins to drop. At which points in the ball’s journey will gravity be the greatest force acting on the ball?
Answer:
If air resistance is taken as negligible, then the ball is in freefall the moment it is thrown so gravity is the only force acting on the object. If air resistance is not negligible then gravity will be the greatest force acting on the ball while it is going up and coming down, because Fair has to be less than gravity at all times otherwise the atmosphere would wither away.
Each tire on a car has a radius of 0.330 m and is rotating with an angular speed of 13.9 revolutions/s. Find the linear speed v of the car, assuming that the tires are not slipping against the ground.
Answer:
the linear speed of the car is 28.83 m/s
Explanation:
Given;
radius of the car, r = 0.33 m
angular speed of each tire, ω = 13.9 rev/s = 13.9 x 2π = 87.35 rad/s
The linear speed of the car is calculated as;
V = ωr
V = 87.35 rad/s x 0.33 m
V = 28.83 m/s
Therefore, the linear speed of the car is 28.83 m/s
An exoplanet has three times the mass and one-fourth the radius of the Earth. Find the acceleration due to gravity on its surface, in terms of g, the acceleration of gravity at Earth's surface. A planet's gravitational acceleration is given by gp = G Mp/r^2p
a. 12.0 g.
b. 48.0 g.
c. 6.00 g.
d. 96.0 g.
e. 24.0 g.
Answer:
b. 48.0 g.
Explanation:
Given;
mass of the exoplanet, [tex]M_p = 3M_e[/tex]
radius of the exoplanet, [tex]r_p = \frac{1}{4} r_e[/tex]
The acceleration due to gravity of the planet is calculated as;
[tex]g_p = \frac{GM_p}{r_p^2} \\\\for \ Earth's \ surface\\\\g = \frac{GM_e}{r_e^2} \\\\G = \frac{gr_e^2}{M_e} = \frac{g_pr_p^2}{M_p} \\\\\frac{gr_e^2}{M_e} = \frac{g_p(\frac{r_e}{4}) ^2}{3M_e} \\\\\frac{gr_e^2}{M_e} = \frac{g_pr_e ^2}{16\times 3M_e} \\\\g = \frac{g_p}{48} \\\\g_p = 48 \ g[/tex]
Therefore, the correct option is b. 48.0 g
A reaction requires 1.5 mL of ammonia if it occurs at 1.65 atm and 23 degrees celsius. If the temperature is changed to 30 degrees celsius, what will the new pressure be if the volume remains the same?
Answer: The new pressure will be 1.69 atm
Explanation:
Gay-Lussac's law states that the pressure of the gas is directly proportional to the temperature of the gas at constant volume and the number of moles.
Mathematically,
[tex]P\propto T[/tex] (At constant volume and number of moles)
OR
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex] .....(1)
[tex]P_1\text{ and }T_1[/tex] are the pressure and temperature of the gas
[tex]P_2\text{ and }T_2[/tex] are the final pressure and temperature of the gas
We are given:
[tex]P_1=1.65atm\\T_1=23^oC=[23+273]K=296K\\V_2=?mL\\T_2=30^oC=[30+273]K=303K[/tex]
Putting values in equation 1, we get:
[tex]\frac{1.65atm}{296K}=\frac{P_2}{303K}\\\\P_2=\frac{1.65\times 303}{296}\\\\P_2=1.69atm[/tex]
Hence, the new pressure will be 1.69 atm
Two oppositely charged objects are separated by a small distance. The objects are then moved three times farther apart from each other. Which of the following statements best describes what happens to the electrical force between the objects?
A: The force of attraction increases
B: The force of attraction decreases
C: The force of attraction stays the same
D: The force of attraction becomes a force of repulsion
The statement best describes what happens to the electrical force between the objects when moved three times farther apart from each other is the force of attraction decreases. The correct option is B.
What is force of attraction?
The objects when placed at a distance, they are attracted by the gravitational force of attraction.
Gravitational force of attraction is directly proportional to the product of masses and inversely proportional to the square of distance between them.
Two oppositely charged objects are separated by a small distance. The objects are then moved three times farther apart from each other.
Force is indirectly proportional to the distance. So, when the distance increases the force of attraction decreases.
Thus, the correct option is B.
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